We introduce the generalized devilís lenses (GDLs) as a new family of diffractive kinoform lenses whose structure
is based on the generalized Cantor set. The focusing properties of different members of this family are analyzed. It
is shown that under plane wave illumination the GDLs give a single main focus surrounded by many subsidiary
foci. It is shown that the total number of subsidiary foci is higher than the number of foci corresponding to
conventional devilís lenses; however, the self-similar behavior of the axial irradiance is preserved to some
extent.